Antenna array including virtual antenna elements

ABSTRACT

A method and associated system for effectively increasing the number of antenna elements within a multi-element antenna system through computation of a response of “virtual” antenna elements located along an antenna array. The physical elements of the array are positioned sufficiently near each other to enable synthesis of a polynomial or other mathematical expression characterizing the response of the array to receipt of an incident waveform. Values of the responses associated with the virtual antenna elements of the array may then be determined through evaluation of the synthesized polynomial or other expression. The resultant array response values associated with the virtual and physical elements of the array are then provided to an associated receiver for processing.

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority under 35 U.S.C. §119(e) to U.S.Provisional Application No. 60/405,285 entitled ANTENNA ARRAY INCLUDINGVIRTUAL ANTENNA ELEMENTS, filed Aug. 21, 2002, which is incorporatedherein by reference in its entirety.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to a multi-element antenna receiverfor radio communication systems, and more particularly to signalprocessing for multiple receive antennas of an associated receiver.

[0004] 2. Background Information

[0005] It has recently been proposed that both the performance andcapacity of existing wireless systems could be improved through the useof so-called “smart” antenna techniques. In particular, it has beensuggested that such techniques, coupled with space-time signalprocessing, could be utilized both to combat the deleterious effects ofmultipath fading of a desired incoming signal and to suppressinterfering signals. In this way both performance and capacity ofdigital wireless systems in existence or being deployed (e.g.,CDMA-based systems, TDMA-based systems, WLAN systems, and OFDM-basedsystems such as IEEE 802.11a/g) may be improved.

[0006] It is anticipated that smart antenna techniques will beincreasingly utilized both in connection with deployment of base stationinfrastructure and mobile subscriber units (e.g, handsets) in cellularsystems in order to address the increasing demands being placed uponsuch systems. These demands are arising in part from the shift underwayfrom current voice-based services to next-generation wireless multimediaservices and the accompanying blurring of distinctions among voice,video and data modes of transmission. Subscriber units utilized in suchnext-generation systems will likely be required to demonstrate highervoice quality relative to existing cellular mobile radio standards aswell as to provide high-speed data services (e.g., as high as 10Mbits/s). Achieving high speed and high quality of service, however, iscomplicated because it is desireable for mobile subscriber units to besmall and lightweight, and to be capable of reliably operating in avariety of environments (e.g., cellular/microcellular/picocellular,urban/suburban/rural and indoor/outdoor). Moreover, in addition tooffering higher-quality communication and coverage, next-generationsystems are desired to more efficiently use available bandwidth and tobe priced affordably to ensure widespread market adoption.

[0007] In many wireless systems, three principal factors tend to accountfor the bulk of performance and capacity degradation: multipath fading,delay spread between received multipath signal components, andco-channel interference (CCI). As is known, multipath fading is causedby the multiple paths which may be traversed by a transmitted signal enroute to a receive antenna. The signals from these paths add togetherwith different phases, resulting in a received signal amplitude andphase that vary with antenna location, direction and polarization, aswell as with time (as a result of movement through the environment).Increasing the quality or reducing the effective error rate in order toobviate the effects of multipath fading has proven to be extremelydifficult. Although it would be theoretically possible to reduce theeffects of multipath fading through use of higher transmit power oradditional bandwidth, these approaches are often inconsistent with therequirements of next-generation systems.

[0008] As mentioned above, the “delay spread” or difference inpropagation delays among the multiple components of received multipathsignals has also tended to constitute a principal impediment to improvedcapacity and performance in wireless communication systems. It has beenreported that when the delay spread exceeds approximately ten percent(10%) of the symbol duration, the resulting significant intersymbolinterference (ISI) generally limits the maximum data rate. This type ofdifficulty has tended to arise most frequently in narrowband systemssuch as the Global System for Mobile Communication (GSM).

[0009] The existence of co-channel interference (CCI) also adverselyaffects the performance and capacity of cellular systems. Existingcellular systems operate by dividing the available frequency channelsinto channel sets, using one channel set per cell, with frequency reuse.Most time division multiple access (TDMA) systems use a frequency reusefactor of 7, while most code division multiple (CDMA) systems use afrequency reuse factor of 1. This frequency reuse results in CCI, whichincreases as the number of channel sets decreases (i.e., as the capacityof each cell increases). In TDMA systems, the CCI is predominantly fromone or two other users, while in CDMA systems there may exist manystrong interferers both within the cell and from adjacent cells. For agiven level of CCI, capacity can be increased by shrinking the cellsize, but at the cost of additional base stations.

[0010] The impairments to the performance of cellular systems of thetype described above may be at least partially ameliorated by usingmulti-element antenna systems designed to introduce a diversity gaininto the signal reception process. There exist at least three primarymethods of effecting such a diversity gain through decorrelation of thesignals received at each antenna element: spatial diversity,polarization diversity and angle diversity. In order to realize spatialdiversity, the antenna elements are sufficiently separated to enable lowfading correlation. The required separation depends on the angularspread, which is the angle over which the signal arrives at the receiveantennas.

[0011] In the case of mobile subscriber units (e.g, handsets) surroundedby other scattering objects, an antenna spacing of only one quarterwavelength is often sufficient to achieve low fading correlation. Thispermits multiple spatial diversity antennas to be incorporated within ahandset, particularly at higher frequencies (owing to the reduction inantenna size as a function of increasing frequency). Furthermore, dualpolarization antennas can be placed close together, with low fadingcorrelation, as can antennas with different patterns (for angle ordirection diversity).

[0012] Although increasing the number of receive antennas enhancesvarious aspects of the performance of multi-antenna systems, thenecessity of providing a separate RF chain for each transmit and receiveantenna increases costs. Each RF chain is generally comprised of a lownoise amplifier, filter, downconverter, and analog to digital toconverter (A/D), with the latter three devices typically beingresponsible for most of the cost of the RF chain. In certain existingsingle-antenna wireless receivers, the single required RF chain mayaccount for in excess of 30% of the receiver's total cost. It is thusapparent that as the number of receive antennas increases, overallsystem cost and power consumption may dramatically increase. It wouldtherefore be desirable to provide a technique that effectively providesadditional receive antennas without proportionately increasing systemcosts and power consumption.

SUMMARY OF THE INVENTION

[0013] In one embodiment, the invention can be characterized as amethod, and means for accomplishing the method, for processing a signalreceived by an antenna array, the method including receiving M replicasof the signal, each of the M replicas being received by one of acorresponding M physical antenna elements of the antenna array;determining M responses of the M physical antenna elements to thesignal, each of the M responses corresponding to one of the M physicalantenna elements; and generating, as a function of the M responses, Nresponses to the signal, wherein each of the N responses represents aresponse to the signal at a different spatial location along the antennaarray.

[0014] In another embodiment, the invention can be characterized as anantenna system for receiving a signal comprising: an antenna arrayincluding M physical antenna elements, wherein the M physical antennaelements are spatially arranged to receive one of a corresponding Mreplicas of the signal so as to be capable of generating M replicas ofthe received signal; and an array processing module including M signalprocessing chains, wherein each of the M signal processing chains iscoupled to one of the M physical antenna elements. The array processingmodule is configured to generate N signal response values for theantenna array as a function of the M replicas of the received signal,the N signal response values including at least one virtual antennaresponse value, wherein N is greater than M.

[0015] In a further embodiment, the invention can be characterized as anarray processing module comprising: M signal processing chains whereineach of the M signal processing chains is configured to receive areplica of a received signal from a corresponding one of M physicalantenna elements; and an interpolation module coupled to the M signalprocessing chains, wherein the interpolation module is configured togenerate N signal response values for the antenna array as a function ofthe M replicas of the received signal.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In the accompanying drawings:

[0017]FIG. 1 is a block diagram of a conventional diversity receiver inwhich the signals received by multiple antenna elements are weighted andcombined in order to generate an output signal;

[0018]FIG. 2 is a block diagram of a conventional spatial-temporal (ST)filtering arrangement;

[0019]FIG. 3 is a representation of a multiple-input/multiple-outputantenna arrangement within a wireless communication system;

[0020]FIG. 4 is a block diagram depicting a conventional architecture ofa multiple receive antenna system in the RF domain;

[0021]FIG. 5 is a block diagram representing a digital equivalent to thecircuit of FIG. 4;

[0022]FIG. 6 is a block diagram of a receiver system incorporating anarray processing module in accordance with one embodiment of the presentinvention;

[0023]FIG. 7 is a flow chart illustrating steps carried out by the arrayprocessing module of FIG. 6 when processing a received signal accordingto one embodiment;

[0024]FIG. 8A is an illustrative representation of a specificimplementation of the antenna array of FIG. 6.

[0025]FIG. 8B is

[0026]FIG. 9 is a diagram illustrating a uniform linear antenna arraydisposed to receive a signal;

[0027]FIG. 10 is a block diagram depicting an antenna systemincorporating a virtual-element antenna array established in accordancewith the present invention; and

[0028]FIG. 11 is a flowchart illustrating steps carried out by theantenna system of FIG. 10 according to one embodiment of the presentinvention;

[0029]FIG. 12 is a block diagram depicting another antenna systemincorporating a virtual-element antenna array established in accordancewith another embodiment of the present invention; and

[0030]FIG. 13 is a block diagram depicting yet another antenna systemincorporating a virtual-element antenna array established in accordancewith yet another embodiment of the present invention

DETAILED DESCRIPTION OF THE INVENTION

[0031] In the following description, various aspects of the presentinvention will be described. However, it will be apparent to thoseskilled in the art that the present invention may be practiced with onlysome or all aspects of the present invention. For purposes ofexplanation, specific numbers, materials and configurations are setforth in order to provide a thorough understanding of the presentinvention. However, it will also be apparent to one skilled in the artthat the present invention may be practiced without the specificdetails. In other instances, well known features are omitted orsimplified in order not to obscure the present invention.

[0032] Various operations will be described as multiple discrete stepsperformed in turn in a manner that is most helpful in understanding thepresent invention, however, the order of description should not beconstrued as to imply that these operations are necessarily orderdependent, in particular, the order the steps are presented.Furthermore, the phrase “in one embodiment” will be used repeatedly,however the phrase does not necessarily refer to the same embodiment,although it may.

[0033] The present invention is directed to a method of effectivelyincreasing the number of antenna elements within a multi-element antennasystem through computation of a response of “virtual” antenna elementspositioned among physical elements of an antenna array. In accordancewith several embodiments of the invention, the physical elements of thearray are positioned sufficiently near each other to enable synthesis ofa polynomial or other mathematical expression characterizing theresponse of the array to receipt of an incident waveform. Values of theresponses associated with the virtual antenna elements of the array maythen be determined through evaluation of the synthesized polynomial orother expression. The resultant array response values associated withthe virtual and physical elements of the array may then be provided toan associated receiver for processing.

[0034] In this way the present invention enhances performance withoutinducing the complexity which would be attendant to straightforwardlyincreasing the number of physical antenna elements and associated signalprocessing paths. In a particular embodiment, the present invention maybe used to desirably reduce the complexity, power consumption and costassociated with the deployment of multiple antenna elements upon mobiledevices. This embodiment may be implemented to effectively increase thenumber of antenna elements from M physical elements to greater than Meffective antenna elements. This increase is effected by using availableinterpolation techniques (e.g., Lagrange interpolation) to create a setof virtual antenna elements interposed between the M physical antennaelements and/or using available extrapolation techniques to create avirtual antenna element at an edge of an antenna array.

[0035] The present invention is not limited to mobile devices and mayalso be applied to infrastructure elements (e.g., base stations andaccess points). In addition, the present invention is applicable tonearly all known wireless standards and modulation schemes (e.g., GSM,CDMA2000, WCDMA, WLAN, fixed wireless standards, OFDM and CDMA).

[0036] In order to facilitate appreciation of the principals of theinvention, a brief overview of various conventional multi-elementantenna systems designed to mitigate delay spread, interference andfading effects is provided with reference to FIGS. 1-5.

[0037] Referring first to FIG. 1, shown is a block diagram of aconventional diversity receiver 100 in which the signals received bymultiple antenna elements are weighted and combined in order to generatean output signal. Shown in the conventional diversity receiver 100 are acollection of M antenna elements 102, and coupled with each respectiveantenna element are parallel receive chains 104, 106, 108 that includerespective weighting portions 110, 112, 114. The receive chains 104,106, 108 all couple with a combiner 116 and a combined single 118 exitsfrom the combiner 116.

[0038] With M antenna elements, such an array generally provides anincreased antenna gain of “M” as well as a diversity gain againstmultipath fading dependent upon the correlation of the fading among theantenna elements. In this context the antenna gain is defined as thereduction in required receive signal power for a given average outputsignal-to-noise ratio (SNR), while the diversity gain is defined as thereduction in the required average output SNR for a given bit error rate(BER) with fading.

[0039] For interference mitigation, each of the M antenna elements 102are weighted at the respective weighting portions 110, 112, 114 andcombined in the combiner 116 to maximizesignal-to-interference-plus-noise ratio (SINR). This weighting processis usually implemented in a manner that minimizes mean squared error(MMSE), and utilizes the correlation of the interference to reduce theinterference power.

[0040] Turning now to FIG. 2, a block diagram is shown of a conventionalspatial-temporal (ST) filtering arrangement 200. Shown are a firstantenna 202 and a second antenna 204 respectively coupled to a firstlinear equalizer 206 and a second linear equalizer 208. Outputs of eachof the first and second linear equalizers 206, 208 are coupled to acombiner 210, and an output of the combiner 201 is coupled to anMLSE/DFE portion 212.

[0041] The filtering arrangement of FIG. 2 is designed to eliminatedelay spread using joint space-time processing. In general, since theCCI is unknown at the receiver, optimum space-time (ST) equalizers,either in the sense of a minimum mean square error (MMSE) or maximumsignal-to-interference-plus-noise ratio (SINR), typically include awhitening filter. For example, linear equalizers (LE) 206, 208 thatwhiten the CCI both spatially and temporally, and the filteringarrangement of FIG. 2 are typical of such systems. As shown in FIG. 2,the linear equalizers (LE) 206, 208 are followed by a non-linear filterthat is represented by the MLSE/DFE portion 212, which is implementedusing either a decision feedback equalizer (DFE) or maximum-likelihoodsequence estimator (MLSE).

[0042] As is known to one of ordinary skill in the art, the turboprinciple can also be used to replace the non-linear filters withsuperior performance, but higher computational complexity. Using STprocessing (STP) techniques, SNR gains of up to 4 dB and SINR gains ofup to 21 dB have been reported with a modest number of antenna elements.

[0043] Referring next to FIG. 3, shown is a generic representation of amultiple-input/multiple-output antenna arrangement within a wirelesscommunication system 300. Shown are a transmitter (TX) 302 coupled tomultiple transmit antennas 304, which are shown transmitting a signalvia time varying obstructions 306 to multiple receive antennas 308coupled to a receiver (RX) 310. As shown, multiple antenna elements aredeployed at both the transmitter (TX) 302 and receiver (RX) 310 of thewireless communication system 300.

[0044] In addition to multiple-input/multiple-output antenna (MIMO)arrangements, other antenna arrangements may be categorized, based uponthe number of “inputs” and “outputs” to the channel linking atransmitter and receiver, as follows:

[0045] Single-input/single-output (SISO) systems, which includetransceivers (e.g., mobile units and a base station) with a singleantenna for uplink and down link communications.

[0046] Multi-input/single-output (MISO) systems, which include one ormore receivers, which downlink via multiple antenna inputs, and one ormore transmitters, which uplink via a single antenna output.

[0047] Single-input/multi-output (SIMO) systems, which include one ormore receivers, which downlink via a single antenna input, and one ormore transmitters, which uplink via multiple antenna outputs.

[0048] One aspect of the attractiveness of multi-element antennaarrangements, particularly MIMOs, resides in the significant systemcapacity enhancements that can be achieved using these configurations.Assuming perfect estimates of the applicable channel at both thetransmitter and receiver are available, in a MIMO system with M receiveantennas the received signal decomposes to M independent channels. Thisresults in an M-fold capacity increase relative to SISO systems. For afixed overall transmitted power, the capacity offered by MIMOs scalewith increasing SNR for a large, but practical, number of M of antennaelements.

[0049] In the particular case of fading multipath channels, it has beenfound that the use of MIMO arrangements permits capacity to be scaled bynearly M additional bits/cycle for each 3-dB increase in SNR. This MIMOscaling attribute is in contrast to a baseline configuration,characterized by M=1, which by Shannon's classical formula scales as onemore bit/cycle for every 3-dB of SNR increase. It is noted that thisincrease in capacity that MIMO systems afford is achieved without anyadditional bandwidth relative to the single element baselineconfiguration.

[0050] However, widespread deployment of multi-element antennaarrangements in wireless communication systems (particularly withinwireless handsets) has been hindered by the resultant increase incomplexity and associated increased power consumption, cost and size.These parameter increases result, at least in part, from a requirementin many proposed architectures that a separate receiver chain beprovided for each antenna element.

[0051] For example, FIG. 4 depicts one conventional architecture of amultiple receive antenna system 400 in the RF domain. As shown, theimplementation of FIG. 4 includes a separate receive chain 402, 404, 406for each of M antenna elements, and each receive chain 402, 404, 406includes elements to perform amplification, filtering and mixing. As aconsequence, the cost of implementing the system 400 is higher than thatof implementing a system with a single receive chain. Moreover, addingadditional antenna elements is often prohibited by the added cost, spaceand/or power associated with additional antenna elements.

[0052] The approach exemplified by the system 400 is furtherdisadvantageous because analog phase shifters and variable gainamplifiers are utilized, which renders it relatively expensive andsusceptible to performance degradation as a result of aging, temperaturevariation, and deviation from prescribed tolerances. In addition,because the implementation of FIG. 4 makes use of a phase relationshipbetween the received and transmitted antenna elements (i.e., the pathdifferential delay is maintained throughout each receive processingchain), rigid adherence to tolerances and accurate calibration isrequired in each RF processing chain.

[0053] Referring next FIG. 5, shown is a block diagram representing adigital equivalent to the system 400 of FIG. 4. In general, theperformance of the digital circuit arrangement 500 of FIG. 5 is degradedfor substantially the same reasons as was described above with referenceto FIG. 4. That is, the duplication of an entire receiver chain (i.e.,from RF to baseband) associated with each antenna element leads to anincrease in size, cost, complexity and power consumption. As a result,adding additional antenna elements in multiple receive antenna systemshas heretofore been unsuitable for deployment in the handsets and othermobile terminals used within wireless communication systems.

[0054] Overview and System Architecture

[0055] The present invention is directed to a system and method forimplementing multiple antenna elements within mobile devices in a mannerthat potentially reduces the costs and power consumption which typicallyaccompany multi-element antenna arrangements.

[0056]FIG. 6 is a block diagram of a receiver system 600 incorporatingan array-processing module 610 in accordance with one embodiment of thepresent invention. The array-processing module 610 receives informationfrom M physical antenna elements 614 of an antenna array 618 which has Nelements. In addition to the M physical antenna elements 614, theantenna array 618 also effectively includes a set of virtual (i.e.,non-physical) antenna elements 622. While referring to FIG. 6,simultaneous reference will be made to FIG. 7, which is a flow chartillustrating steps carried out by the array-processing module 610 whenprocessing a signal received by the antenna array 618.

[0057] The array-processing module 610 is operative to synthesize theresponses of the virtual antenna elements 622 to waveforms impingingupon the antenna array 618. These responses, together with the responsesproduced by the M physical antenna elements 614 are then forwarded to areceiver 630 for further processing. In one embodiment, thearray-processing module 610 further processes the responses from boththe virtual antenna elements 622 and the M physical antenna elements 614before forwarding them to the receiver 630.

[0058] In operation, a signal impinges upon the antenna array 618 andeach of the M physical antenna elements 614 receives a replica of thesignal. The array-processing module 610 then receives the M replicas ofthe signal from the M physical antenna elements 614 (Step 700).

[0059] Next, the array-processing module 610 determines a response ofeach of the M physical antenna elements to the signal (Step 702). Asdiscussed further herein, in some embodiments, the response of each ofthe M physical antenna elements 614 is calculated as a function of aweighting parameter that is associated with each M physical antennaelements 614. In other embodiments, the response of each of the Mphysical antenna elements 614 is obtained by sampling each of acorresponding one of the M replicas of the signal.

[0060] After the responses of the M physical antenna elements 614 aredetermined, the array-processing module 610 calculates responses of thevirtual antenna elements 622 to the signal as a function of theresponses of the M physical antenna elements 614 (Step 704). In severalembodiments, the response of each of the virtual antenna elements 622 iscalculated by interpolating and/or extrapolating responses of at leasttwo of the M physical antenna elements 614.

[0061] Thus, the array processing module 610 provides N responses to thesignal, i.e., a response for each element of the antenna array 618 (Step706). The N responses may then be further processed by the arrayprocessing module 610 before being forwarded to the receiver 630.

[0062] Advantageously, the array processing module 610 effectivelyprovides the receiver 630 with an antenna array having N (e.g., five)elements, notwithstanding that only M (e.g., three) physical antennaelements 614 are deployed. As a consequence, the array processing moduleprovides the advantages of an antenna array which has N physicalelements without the associated cost and power consumption typicallyassociated with N receiver chains.

[0063] It should be noted that the array processing module 610 may beimplemented as a set of instructions that are performed in dedicatedhardware, firmware or in software using a processor or other machine toexecute the instructions to accomplish the provided functionality. Itshould also be noted that the array processing module 610 and thereceiver 630 are illustrated as separate blocks in FIG. 6 for purposesof describing specific functions carried out by the array processingmodule 610, but the processing module 610 may share the same hardwareutilized by the receiver: Furthermore, the array processing module 610may be incorporated as part of the receiver 630.

[0064] Turning now to FIGS. 8A and 8B, shown is an illustrativerepresentation of the antenna array 618 exposed to a signal 602 and arepresentation of replicas of the signal received by elements theantenna array 618 as a function of time, respectively. As will bedescribed hereinafter, adjacent ones of the physical antenna elements614 are spatially separated by no more than a distance λ/2, where λrepresents the wavelength of the signal energy received by the antennaarray 618. As shown, the antenna array 618 includes a set of threephysical antenna elements 614 (i.e., M=3) and two virtual antennaelements 622, thereby effectively yielding a 5-element array (i.e.,N=5). As shown in FIG. 8A, as a wave front of the signal 602 approachesthe antenna array 618 from left to right at an angle φ with respect to adirection 604 normal to a the antenna array 618, a first signal replicaS₀ is received at a left most physical antenna element first, and theright most antenna element 614, which is separated from the left mostphysical antenna element 614 by a distance of 4*d, will not receive acorresponding replica S₂ of the signal until 4*(dsin φ/c) seconds later.

[0065] As shown in FIG. 8B, after a delay of 4*(dsin φ/c) seconds theright most physical antenna element 614 receives the replica S₂ of thesignal. As a consequence, after the replica S₂ of the signal is receivedat the right most antenna, the left most antenna has received the signalfor five periods (of dsin φ/c seconds each). As shown, after a delay of4*(dsin φ/c) seconds, a response of the entire antenna array 618 may becalculated by interpolating responses of the physical antenna elements614 to the signal replicas S₀, S₁, S₂.

[0066] The principles of the present invention may be furtherappreciated by reference to various aspects of time-frequency signalprocessing. In this regard it is observed that a filter is characterizedby values of its impulse response, h_(m), spaced regularly with a time Tbetween samples. A linear shift-invariant system is also characterizedby the frequency response: $\begin{matrix}{{H\left( ^{j\quad \omega \quad T} \right)} = {\sum\limits_{m = 0}^{M - 1}{h_{m}^{{- j}\quad m\quad \omega \quad T}}}} & (1)\end{matrix}$

[0067] which is given in equation (1) for a finite length impulseresponse comprised of M samples, represented by {t_(m)}. Consistent withthe well-known sampling theorem, in order to prevent any phaseambiguities from arising it is necessary for the sampling interval (T)and the angular frequency (ω) to be set such that the argument in theexponent of (1) satisfies the relationship ωT≦π.

[0068] Referring now to FIG. 9, a uniform linear antenna array 900 isseen to include a plurality of physical array elements 904. The arrayelements 904 are of element length l, and are mutually separated by anelement distance d. In addition, a signal waveform S impinges upon thelinear antenna array 900 from an angular direction φ. If it is assumedthat the array 900 includes M physical array elements 904 regularlyspaced with a distance d, then these array elements 904 are located atx_(m)=md for m=0, . . . ,M−1. The array 900 may be characterized by anaperture smoothing function which may be expressed as $\begin{matrix}{{W(u)} = {\sum\limits_{m = 0}^{M - 1}{w_{m}^{{- j}\quad m\quad 2\quad {\pi {({u/\lambda})}}d}}}} & (2)\end{matrix}$

[0069] where w_(m) is a weighting parameter associated with each arrayelement, φ is the angle (i.e., the azimuth angle) between broadside ofthe array 900 and the direction of the incident waveform of wavelengthλ, and where the variable u is defined by the expression u=sinφ. In theexemplary embodiment the weights w_(m) define a standard windowingfunction or can be adaptively altered according to specified criteria.

[0070] It may be appreciated that certain aspects of the expression inequation (2) may be derived from the geometry of FIG. 9. Specifically,for an incident waveform originating at an infinite distance from array900, the difference in the distance traveled between two neighboringelements 904 is d sin φ. When this distance is converted to phase angle,the result is the expression in the exponent of equation (2) (where eachwavelength λ of distance traveled corresponds to 2π). In summary,formulation and computation of the array smoothing function of equation(2) involves weighting the responses of all elements of the array 900,summing the weighted responses, and outputting the sum of the weightedresponses.

[0071] It is noted that the aperture smoothing function of equation (2)indicates the manner in which the Fourier transform of the incidentwaveform is “smoothed” or otherwise altered as a consequence ofobservation through a finite aperture. This may be considered analogousto the role of the frequency response characterizing a filteringoperation, which reveals the way in which the spectrum of the receivedsignal is smoothed by such filtering operation.

[0072] Given the analogous relationship between equations (1) and (2),the present invention recognizes that the constraints needing to beimposed upon the parameters in equation (1) to prevent an aliasingcondition from arising in equation (1) permit development of similar“anti-aliasing” constraints in equation (2). In particular, the argumentin the exponent of equation (2) must satisfy the following constraint toensure that an aliasing condition does not arise: $\begin{matrix}{{2\quad \pi \quad \frac{u}{\lambda}d} = {{{k_{x}} \cdot d} \leq \pi}} & (3)\end{matrix}$

[0073] where k_(x)=2πu/λ is the x-component of the wave number.

[0074] The relationship between the array pattern for theone-dimensional array of FIG. 9 and a filter frequency response may nowbe expressed as: $\begin{matrix}{{\left. \omega\leftrightarrow k_{x} \right. = {2\quad \pi \quad \frac{u}{\lambda}}}\left. T\leftrightarrow d \right.\left. h_{n}\leftrightarrow w_{n} \right.\left. \left\{ t_{m} \right\}\leftrightarrow M \right.} & (4)\end{matrix}$

[0075] In view of equation (4), the time-frequency sampling constraintT≦π/ω_(max) may be expressed as a spatial domain sampling constraintd≦λ_(min)/2.

[0076] In accordance with the invention, it has been recognized by theinventors that the relationships set forth in equation (4) allow timedomain interpolation techniques to be applied to linear antenna arraysin order to enable computation of the responses of “virtual antennas”that may be either interposed between the physical elements of the arrayor positioned at an edge of an array. That is, application ofinterpolation and extrapolation techniques to the responses generated bythe physical elements of a linear array (e.g., the array 618, 900)permits derivation of responses of various virtual antennas among thephysical elements of the array, (e.g., the array 618, 900). As wasmentioned above, this concept is illustratively represented by theplacement of virtual antenna elements 622 among the physical antennaelements 614 in FIG. 8A.

[0077] Various well known time domain interpolation and extrapolationtechniques may be used to generate the responses of the virtual arrayelements 622 on the basis of the responses of the physical elements 614,904 of the array 618, 900. It may be appreciated that such “sampling”within the spatial domain effectively amounts to an estimation of anarray response given a specific antenna geometry, input signal carrierfrequency and angle of incidence of the received waveform. Time domainestimation approaches such as, for example, Lagrange techniques andRadial Basis Function (RBF) networks may be utilized for interpolationand extrapolation, however, Lagrange techniques are less effective thanRBF techniques for extrapolating. Since RBF networks may be used tosolve nonlinearly separable classification problems, such networks canalso be employed to perform interpolation and/or extrapolationoperations upon a set of data points in a multi-dimensional space. Thoseskilled in the art will appreciate that other interpolation andextrapolation techniques may be utilized in a manner consistent with theinvention, and that the above techniques should be consideredillustrative and not of exclusive utility. Those of ordinary skill inthe art will also appreciate that the effectiveness of interpolating andextrapolating depends upon the correlation among the antennas.

[0078] A specific example of the use of interpolation and extrapolationtechniques to determine the responses of virtual antennas distributedthroughout an array of physical antenna elements will now be provided.Considering equation (7) below, a polynomial of degree n may beconstructed so as to coincide with a given function at n+1 uniform ornon-uniform points using Lagrange interpolation. For present purposes,the Lagrange interpolation theorem contemplates that given n+1 distinct(real or complex) points, z₀, z₁, . . . , z_(n) and n+1 (real orcomplex) values, w₀, w₁, . . . , w_(n), there exists a unique polynomialp_(n)(z)ε

_(n) for which

p _(n)(z _(i))=w_(i), ∀_(i)=0,1, . . . , n.  (5)

[0079] In view of the transformations into the spatial domain set forthin (2)-(4), the expression in (5) may be used to derive a Lagrangespatial interpolation theorem:

p _(m)(d _(i))=w _(i), ∀_(i)=0,1, . . . ,m.  (6)

[0080] where d_(i) is the spacing between adjacent elements of anantenna array.

[0081] Lagrange interpolation may be alternately characterized as amethod of finding a polynomial y=ƒ(x) which passes through a specifiedset of n points {x(i), y(i)}, 1≦i≦n, in a plane. Only a single conditionis placed upon the points; namely, that all points should have differentx-coordinates. That is, x(i)=x(j) if and only if i=j. Such a polynomialis defined as follows. For 1≦j≦n, let $\begin{matrix}{{p\left( {j,x} \right)} = {\prod\limits_{i \neq j}^{\quad}\left\{ {x - {x(i)}} \right\}}} & (7)\end{matrix}$

[0082] The expression in equation (7) is zero at every one of the npoints except x(j), where it is nonzero. Next, let $\begin{matrix}{y = {{f(x)} = {\sum\limits_{j = 1}^{n}{{y(j)}{{p\left( {j,x} \right)}/{p\left( {j,{x(j)}} \right)}}}}}} & (8)\end{matrix}$

[0083] The polynomial in equation (8) is nominally of degree n−1, andhas the property that ƒ(x(i))=y(i) for every i. As an example, apolynomial is constructed using equation (8) on the basis of two points{x(1),y(1)} and {x(2),y(2)}. In this case, p(1,x)=x−x(2), and p(2,x)=x−x(1). Continuing: $\begin{matrix}{y = {f(x)}} & (9) \\{\quad {= {{{{y(1)}\left\lbrack {x - {x(2)}} \right\rbrack}/\left\lbrack {{x(1)} - {x(2)}} \right\rbrack} + {{{y(2)}\left\lbrack {x - {x(1)}} \right\rbrack}/\left\lbrack {{x(2)} - {x(1)}} \right\rbrack}}}} & (10) \\{\quad {= {{{x\left\lbrack {{y(1)} - {y(2)}} \right\rbrack}/\left\lbrack {{x(1)} - {x(2)}} \right\rbrack} + {\left\lbrack {{{x(1)}{y(2)}} - {{x(2)}{y(1)}}} \right\rbrack/\left\lbrack {{x(1)} - {x(2)}} \right\rbrack}}}} & \quad \\{{y - {y(2)}} = {{{x\left\lbrack {{y(1)} - {y(2)}} \right\rbrack}/\left\lbrack {{x(1)} - {x(2)}} \right\rbrack} +}} & (11) \\{\quad {\left\lbrack {{{x(2)}{y(2)}} - {{x(2)}{y(1)}}} \right\rbrack/\left\lbrack {{x(1)} - {x(2)}} \right\rbrack}} & \quad \\{\quad {= {{{x\left\lbrack {{y(1)} - {y(2)}} \right\rbrack}/\left\lbrack {{x(1)} - {x(2)}} \right\rbrack} -}}} & \quad \\{\quad {{{{x(2)}\left\lbrack {{y(1)} - {y(2)}} \right\rbrack}/{\left\lbrack {{x(1)} - {x(2)}} \right\rbrack \left\lbrack {y - {y(2)}} \right\rbrack}}/\left\lbrack {{y(1)} - {y(2)}} \right\rbrack}} & \quad \\{\quad {= {\left\lbrack {x - {x(2)}} \right\rbrack/\left\lbrack {{x(1)} - {x(2)}} \right\rbrack}}} & \quad\end{matrix}$

[0084] It is observed that equation (11) corresponds to an equation of aline through the two points {x(1),y(1)} and {x(2),y(2)}.

[0085] Consider now a numerical example involving three points (−2,5),(0,1), and (3,7). Then

p(1,x)=(x−0)(x−3)=x²−3x

p(2,x)=(x+2)(x−3)=x² −x−6

p(3, x)=(x+2)(x−0)=x ²+2x  (12)

[0086] Now $\begin{matrix}\begin{matrix}{y = {f(x)}} \\{= {{5{\left( {x^{2} - {3x}} \right)/10}} + {1{\left( {x^{2} - x - 6} \right)/\left( {- 6} \right)}} + {7{\left( {x^{2} + {2x}} \right)/15}}}} \\{= {{{4/5}x^{2}} - {{2/5}x} + 1}} \\{= \frac{{4x^{2}} - {2x} + 5}{5}}\end{matrix} & (13)\end{matrix}$

[0087] This may be checked as follows:

ƒ(−2)=(16+4+5)/5=5

ƒ(0)=(0+0+5)/5=1

ƒ(3)=(36−6+5)/5=7.  (14)

[0088] Referring again to FIG. 8, the spatial interpolation contemplatedby equation (6) may be applied to develop the array 618. In particular,the three physical antenna elements 614 (i.e., M=3) of the array 618 maybe extended into a five-element antenna system (i.e., N=2×3−1=5) byderiving a suitable polynomial using Lagrange spatial interpolation (itbeing understood that different interpolation schemes may yielddifferent numbers of virtual antennas given M physical antennas). Theresponses of the virtual antennas 622 of the array 618 may then beobtained by evaluating the polynomial at desired locations between thephysical antennas of the array 618. The array 618, which contains threephysical elements 614 and two virtual elements 622, will have the samestatistical properties in a correlated environment as a linear antennaarray containing five physical elements. This property enablesconstruction of a sparse array based upon a conventional array havingregular spacing between elements. In the example of FIG. 8, the antennaspacing, d_(m)=λ/2 and d_(n)=λ/4, is uniform but such uniformity is nota required criteria. That is, the teachings of the present invention mayalso be used to construct a random array, in one or more dimensions, inwhich a certain fraction of the elements are removed at random.

[0089] The antenna element spacing (i.e., spatial sampling) can beoptimized using the criteria of minimization of the maximum sidelobeenergy, or minimization of the sidelobe energy. By optimizing both theantenna element spacing and the array weighting function, it is possibleto construct a non-uniform antenna array with optimal spatialsuppression. This optimization may be effected by using an optimizationcriteria such as optimal interference suppression. For example, apredefined training sequence applied to the array could be utilized asweighting criteria in connection with optimization of the weightsassociated with the array elements.

[0090] Turning now to FIG. 10, there is shown an antenna system 1000incorporating a virtual-element antenna array 1010 established inaccordance with the present invention. The array 1010 includes Mphysical antenna elements 1014 and one or more virtual antenna elements1018 which may be positioned among the M physical antenna elements 1014.A down conversion portion 1004 is coupled to the M physical antennaelements 1014, and is operable to convert signal replicas received ateach of the M physical antenna elements 1014 from RF to baseband.

[0091] In this embodiment, the down conversion portion 1004 is withinthe array-processing module 1002 and is coupled to each of M physicalsignal processing chains 1040, which receive baseband replicas of thereceived signal from the down conversion portion 1004. As shown, the Mphysical antenna elements 1040 are coupled to a summing portion 1050 viathe M physical signal processing chains 1040.

[0092] The array-processing module 1002 further includes an adaptiveweighting module 1022 and an interpolation module 1030 operativelyconnected to a first plurality of physical weighting elements 1034 and asecond plurality of physical weighting elements 1038, respectively. Asshown, each of the first plurality of physical weighting elements 1034are coupled with a corresponding one of the M physical signal processingchains 1040. Each of the second plurality of physical weighting elements1038 are also coupled with a corresponding one of the M physical signalprocessing chains 1040, but are coupled “down stream” along the physicalprocessing chains 1040 relative to the first plurality of physicalweighting elements 1034. In the present embodiment, the interpolationmodule 1030 is also operatively connected to one or more virtualweighting elements 1042, which are coupled to the summing portion 1050.

[0093] The first plurality of physical weighting elements 1034 areiteratively adjusted in accordance with predefined algorithms executedby the adaptive weighting module 1022. Similarly, the second pluralityof physical weighting elements 1038 and the one or more virtualweighting elements 1042 are iteratively adjusted in accordance withpredefined algorithms executed by the interpolation module 1030. Whilereferring to FIG. 10, simultaneous reference will be made to FIG. 11,which is a flowchart illustrating steps carried out by the antennasystem 1600 according to one embodiment of the present invention.

[0094] It should be recognized that the interpolation module 1030 is notlimited to performing interpolation calculations. As one of ordinaryskill in the art will appreciate, the interpolation module 1030 may beused to extrapolate response values of virtual antenna elements fromresponse values of physical antenna elements; thus a response value fora virtual antenna element located at an end of an antenna array may becalculated.

[0095] During operation of the antenna system 1000, each of the Mphysical antenna elements 1014 receives a replica of a signal (Step1100). As a consequence, each of the physical signal processing chains1040 receives one of M replicas of the signal. Based on the M replicasof the signal, the adaptive weighting module 1022 establishes Mcorresponding physical weighting parameters (Step 1102). Specifically,the physical weighting parameters (that are to be ascribed to the firstplurality of physical weighting elements 1034) are initially determinedby way of a constraint adaptive algorithm executed by the adaptiveweighting module 1022. Such an adaptive algorithm processes the input tothe antenna array 1010 (i.e., the M replicas of the signal) andcalculates a set of weighting parameters (e.g., complex values) to beassociated with the first set of physical weighting elements 1034.

[0096] After execution of a number of iterations of the adaptivealgorithm by the adaptive weighting module 1022, a response value foreach of the M physical antenna elements 1014 is determined as a functionof a corresponding one of the weighting parameters (Step 1104) using,for example, equation 2. The M response values (corresponding to the Mphysical antenna elements 1014) are then interpolated by any of thetechniques previously discussed in order to calculate the response valueof the one or more virtual antenna elements 1018 (Step 1106). Theresulting response values for the one or more virtual antenna elements1018 and the response values for the M physical antenna elements 1014collectively provide an array response.

[0097] The resulting array response is then used by the interpolationmodule 1030 to calculate a new set of weight parameters for the physicalweighting elements 1038 and virtual weighting element(s) 1042 (Step1108). The weighted signals from the physical weighting elements 1038and virtual weighting element(s) 1042 are then combined at the summingportion 1050, which provides a representation of the received signal atan output of the antenna-processing module 1002.

[0098] Referring next to FIG. 12, there is shown an antenna system 1200incorporating a virtual-element antenna array 1210 established inaccordance with another embodiment of the present invention. The antennaarray 1210 includes N total antenna elements, which includes first,second and third physical antenna elements 1214, 1216, 1217 as well asfirst and second virtual antenna elements 1218, 1220. The first virtualantenna element 1218 is shown interposed between the first and thesecond physical antenna elements 1214, 1216 and the second virtualantenna element 1220 is shown at an edge of the antenna array 1210adjacent to the third physical antenna element 1217. The first, secondand third physical antenna elements 1214, 1216, 1217 are a subset of acollection of M physical antenna elements, which are a subset of the Ntotal antenna elements in the antenna array 1210.

[0099] Coupled to each of the M physical antenna elements is acorresponding one of M physical signal processing chains 1240, which areshown within an array-processing module 1202. As shown, each of the Mphysical processing chains 1240 terminates at a summing portion 1250,and along each of the M physical processing chains 1240 is a physicalweighting element 1238.

[0100] The array-processing module 1202 also includes first and secondvirtual signal generators 1244, 1246, which are coupled to a first andsecond virtual signal processing chains 1248, 1249, respectively. Thefirst and second virtual signal processing chains 1248, 1249 terminateat the summing portion 1250 and include first and second virtualweighting elements 1242, 1243, respectively.

[0101] In this embodiment, an interpolation module 1230 in thearray-processing module 1202 is coupled to each of the M physical signalprocessing chains 1240 so that it is capable of sampling a signalreplica received at each of the M physical antenna elements. Theinterpolation module 1230 is also coupled to the first and secondvirtual signal generators 1244, 1246, which function to generate signalsrepresentative of the received signal at spatial locations of the firstand second virtual antenna elements 1218, 1220, respectively.

[0102] It is contemplated that the processing performed by thearray-processing module 1200 may be performed at RF and/or at baseband.The interpolation module 1230, for example, may sample and operate on RFsignals, while the adaptive weighting portion 1222 calculates weightparameters for baseband signals. Alternatively, both the interpolationmodule 1230 and the adaptive weighting module 1222 may operate in the RFdomain. For purposes of describing the operation of the antenna system1200, however, it is assumed that the interpolation module 1230 and theadaptive weighting module 1222 are operating in the baseband domain,i.e., replicas of a received signal are down converted by a downconversion portion (not shown) before being sampled.

[0103] In operation, when a received signal impinges upon the antennaarray 1210, each of the M physical antenna elements receives acorresponding one of M replicas of the signal. The interpolation module1230 then determines a response of each of the M physical antennaelements to the signal by sampling each of a corresponding one of the Mreplicas of the signal.

[0104] The interpolation module 1230 then calculates a response of thefirst and second virtual antenna elements 1218, 1220 as a function ofthe M sampled signal replicas. This calculation involves interpolatingresponses of the first and second physical antenna elements 1214, 1216to determine a response of the first virtual antenna element 1218, andextrapolating responses of at least a portion of the M physical antennaelements (including the third physical antenna element 1217) todetermine a response of the second virtual antenna element 1220. Thesecalculations may be performed according to any of the techniquespreviously discussed to calculate the response values of the first andsecond virtual antenna elements 1218, 1220. One of ordinary skill in theart will appreciate that there must be a sufficient correlation(established by antenna spacing) among the M physical antenna elementsbefore the interpolation and extrapolation techniques are effective.

[0105] In the present embodiment, the amplitude of the M sampled signalreplicas is assumed to be the same across the antenna array 1210, andonly phase values of the first and second virtual antenna elements 1218,1220 are calculated by one of the previously discussed techniques. Inother embodiments, however, signal amplitude and phase information forthe M sampled signal replicas is utilized to calculate response valuesfor virtual antenna elements.

[0106] The interpolation module 1230 then provides each of the first andsecond virtual signal generators 1244, 1246 with separate phaseinformation, which is utilized by the virtual signal generators 1244,1246 to generate a first and second virtual antenna responses for thefirst and second antenna elements 1218, 1220, respectively. In thepresent embodiment, the phase information is a phase offset, which whenmultiplied by a signal replica received at a physical antenna element,provides a virtual antenna element response for a virtual antennaelement adjacent to the physical antenna element.

[0107] As shown in FIG. 12, for example, the replica of the signalreceived at the first physical antenna element 1214 is provided to thefirst virtual signal generator 1244 where the replica of the signal ismultiplied by a phase offset to generate a response to the first virtualantenna element 1218, which represents a response to the received signalat the spatial location of the first virtual antenna element 1218.Similarly, the replica of the signal received at the third physicalantenna element 1217 is provided to the second virtual signal generator1246 where the replica of the signal is multiplied by a phase offset togenerate a response to the second virtual antenna element 1218, whichrepresents a response to the received signal at the spatial location ofthe second virtual antenna 1220.

[0108] As a result, the array-processing module 1202 generates Nresponses to the received signal as a function of M received signalreplicas; namely, the M responses generated from the M physical antennaelements and the calculated responses of the first and second virtualantenna elements 1218, 1220.

[0109] In the present embodiment, each of the M responses to the signalis weighted by a weighting parameter (calculated by the adaptiveweighting module 1222) at a corresponding one of the physical weightingelements 1238, and the responses to the first and second virtual antennaelements 1218, 1220 are weighted by a weighting parameter at the firstand second virtual weighting elements 1242, 1243, respectively. Theweighted responses of the M physical antenna elements and the weightedresponses of the first and second virtual antenna elements 1218, 1220are then combined at the summing portion 1250 to form a signalrepresentative of the signal received at the antenna array 1210, whichis provided as an output of the array processing module 1202.

[0110] Referring next to FIG. 13, there is shown an antenna system 1300incorporating a virtual-element antenna array 1310 established inaccordance with yet another embodiment of the present invention. In thisembodiment, the antenna system 1300 is the same as the antenna system1200 except that a third virtual antenna element 1324 is in place of thesecond physical antenna element 1216. Additionally, the physicalprocessing chain 1240 associated with the second physical antennaelement 1216 has been replaced with a third virtual processing chain1352, which is coupled to a third virtual signal generator 1350 andincludes a third virtual weighting element 1354

[0111] As shown, in this embodiment the third virtual signal generator1350 generates a response to the third virtual antenna element 1324 bymultiplying a replica of a signal received at a first physical antennaelement 1314 by a phase offset provided by the interpolation module1330. As a consequence, responses of two adjacent virtual antennaelements 1318, 1324 are generated for subsequent processing. One ofordinary skill in the art will appreciate that the two adjacent virtualantenna elements 1318, 1324 must be close enough to at least twocorrelated physical antenna elements of the antenna array 1310 toprovide an accurate representation of responses of the two adjacentvirtual antennas 1318, 1324 to a received signal.

[0112] The foregoing description, for purposes of explanation, usedspecific nomenclature to provide a thorough understanding of theinvention. However, it will be apparent to one skilled in the art thatthe specific details are not required in order to practice theinvention. In other instances, well-known circuits and devices are shownin block diagram form in order to avoid unnecessary distraction from theunderlying invention. Thus, the foregoing descriptions of specificembodiments of the present invention are presented for purposes ofillustration and description. They are not intended to be exhaustive orto limit the invention to the precise forms disclosed, obviously manymodifications and variations are possible in view of the aboveteachings. The embodiments were chosen and described in order to bestexplain the principles of the invention and its practical applications,to thereby enable others skilled in the art to best utilize theinvention and various embodiments with various modifications as aresuited to the particular use contemplated.

What is claimed is:
 1. A method for processing a signal received by anantenna array comprising: receiving M replicas of the signal, each ofthe M replicas being received by one of a corresponding M physicalantenna elements of the antenna array; determining M responses of the Mphysical antenna elements to the signal, each of the M responsescorresponding to one of the M physical antenna elements; and generating,as a function of the responses of the M physical antenna elements to thesignal, N responses to the signal, respectively associated with Nspatial locations along the antenna array, wherein at least one of the Nspatial locations is not coincident with a location of any of the Mphysical antenna elements.
 2. The method of claim 1 wherein N−Mresponses of the N responses are associated with virtual antennaelements located among the physical antenna elements.
 3. The method ofclaim 2 wherein at least one of the N−M responses is generated byinterpolating at least two of the M responses.
 4. The method of claim 2wherein at least one of the N−M responses is generated by extrapolatingfrom at least two of the M responses.
 5. The method of claim 1including: down converting the M replicas of the signal from radiofrequency (RF) to baseband prior to the determining the M responses ofthe of the M physical antenna elements.
 6. The method of claim 1 whereinthe determining includes calculating M physical weighting parameters,wherein the response of each of the M physical antenna elements isdetermined as a function of a corresponding one of the M physicalweighting parameters.
 7. The method of claim 1 wherein the determiningincludes sampling each of the M replicas such that each of the Mresponses comprises a sample of a corresponding one of the M replicas ofthe signal.
 8. The method of claim 1, further including: weighting eachof the N responses to the signal, thereby generating N weightedresponses; and combining the N weighted responses, thereby generating arepresentation of the signal.
 9. The method of claim 1, wherein thesignal complies with a communication protocol selected from the groupconsisting of: orthogonal frequency division multiplexing (OFDM), timedivision multiple access (TDMA), code division multiple access (CDMA),gaussian minimum shift keying (GMSK), complementary code keying (CCK),quadrature phase shift keying (QPSK), frequency shift keying (FSK),phase shift keying (PSK), and quadrature amplitude modulation (QAM). 10.An antenna system for receiving a signal comprising: an antenna arrayincluding M physical antenna elements, wherein the M physical antennaelements are spatially arranged to receive one of a corresponding Mreplicas of the signal so as to be capable of generating M replicas ofthe received signal; and an array processing module including M signalprocessing chains, wherein each of the M signal processing chains iscoupled to one of the M physical antenna elements; wherein the arrayprocessing module is configured to generate N signal response values forthe antenna array as a function of the M replicas of the receivedsignal; wherein the N signal response values include at least onevirtual antenna response value, wherein N is greater than M.
 11. Theantenna system of claim 10 wherein the array processing module includes:a weighting module coupled to the M signal processing chains wherein theweighting module is configured to calculate M physical weightingparameters as a function of the M replicas of the received signal,wherein each of the M physical weighting parameters is associated with acorresponding one of the M physical antenna elements; and aninterpolation module coupled to the M signal processing chains, whereinthe interpolation module is configured to generate the N signal responsevalues for the antenna array as a function of the M physical weightingparameters.
 12. The antenna system of claim 11, wherein theinterpolation module is configured to calculate the M signal responsevalues as a function of the M physical weighting parameters andinterpolate at least two of the M signal response values to provide thevirtual antenna response value.
 13. The antenna system of claim 10wherein the array-processing module includes: an interpolation modulecoupled to the M signal processing chains, wherein the interpolationmodule is configured to generate the N signal response values for theantenna array as a function of the M replicas of the signal; a weightingmodule coupled to the M signal processing chains wherein the weightingmodule is configured to calculate N weighting parameters as a functionof the N signal response values.
 14. The antenna system of claim 10wherein the N signal response values for the antenna array include Msignal response values corresponding to the M physical antenna elements,wherein the virtual antenna response value corresponds to a virtualantenna element positioned within a distance of λ/2 of at least two ofthe physical antenna elements, wherein λ represents a wavelength of acarrier frequency of the signal.
 15. The antenna system of claim 14wherein the virtual antenna element is interposed between at least twoof the M physical antenna elements.
 16. The antenna system of claim 14wherein the virtual antenna element is located at an edge of the antennaarray.
 17. The antenna system of claim 10 wherein the at least two ofthe M physical antenna elements are spatially separated by no more thana distance of λ/2, wherein λ represents a wavelength of a carrierfrequency of the signal.
 18. The antenna system of claim 10 wherein thearray processing module is configured to generate N signal responsevalues for the antenna array as a function of the M replicas of thereceived signal by methodologies selected from the group consisting ofinterpolation and extrapolation.
 19. The antenna system of claim 10wherein the signal complies with a communication protocol selected fromthe group consisting of: orthogonal frequency division multiplexing(OFDM), time division multiple access (TDMA), code division multipleaccess (CDMA), gaussian minimum shift keying (GMSK), complementary codekeying (CCK), quadrature phase shift keying (QPSK), frequency shiftkeying (FSK), phase shift keying (PSK), and quadrature amplitudemodulation (QAM).
 20. A receiver system for receiving a signalcomprising: an antenna array including M physical antenna elements forreceiving M replicas of the signal, each of the M replicas beingreceived by a corresponding one of the M physical antenna elements;means for determining a response of each of the M physical antennaelements to the signal; and means for generating, as a function of theresponses of the M physical antenna elements to the signal, N responsesto the signal, respectively associated with N spatial locations alongthe antenna array, wherein at least one of the N spatial locations isnot coincident with a location of any of the M physical antennaelements.
 21. The receiver system of claim 20 wherein N−M responses ofthe N responses are associated with virtual antenna elements locatedamong the physical antenna elements.
 22. The receiver system of claim 21wherein the means for generating includes means for generating at leastone of the N−M responses by interpolating at least two of the Mresponses.
 23. The receiver system of claim 21 wherein the means forgenerating includes means for generating at least one of the N−Mresponses by extrapolating from at least two of the M responses.
 24. Thereceiver system of claim 20 wherein the M physical antenna elements arespatially separated by no more than a distance of λ/2, wherein λrepresents a wavelength of a carrier frequency of the signal.
 25. Thereceiver system of claim 20 wherein the means for determining includesmeans for calculating M physical weighting parameters, wherein theresponse of each of the M physical antenna elements is determined as afunction of a corresponding one of the M physical weighting parameters.26. The receiver system of claim 20 wherein the means for determiningincludes means for sampling each of the M replicas being received by oneof a corresponding M physical antenna elements, wherein the response ofeach of the M physical antenna elements is a sample of a correspondingone of the M replicas of the signal.
 27. The receiver system of claim20, including: means for weighting each of the N responses to the signalto produce N weighted responses; and means for combining the N weightedresponses to produce a representation of the signal.
 28. The receiversystem of 20, wherein the signal complies with a communication protocolselected from the group consisting of: orthogonal frequency divisionmultiplexing (OFDM), time division multiple access (TDMA), code divisionmultiple access (CDMA), gaussian minimum shift keying (GMSK),complementary code keying (CCK), quadrature phase shift keying (QPSK),frequency shift keying (FSK), phase shift keying (PSK), and quadratureamplitude modulation (QAM).
 29. An array processing module comprising: Msignal processing chains wherein each of the M signal processing chainsis configured to receive a replica of a received signal from acorresponding one of M physical antenna elements; and an interpolationmodule coupled to the M signal processing chains, wherein theinterpolation module is configured to generate N signal response valuesfor the antenna array as a function of the M replicas of the receivedsignal.
 30. The array processing module of claim 29 including: aweighting module coupled to the M signal processing chains wherein theweighting module is configured to calculate M physical weightingparameters as a function of the M replicas of the received signal,wherein each of the M physical weighting parameters is associated with acorresponding one of the M physical antenna elements; wherein theinterpolation module is configured to generate the N signal responsevalues for the antenna array as a function of the M physical weightingparameters.
 31. The array processing module of claim 29 including: aweighting module coupled to the M signal processing chains wherein theweighting module is configured to calculate N weighting parameters as afunction of the N signal response values; and N weighting elementsconfigured to receive the N signal response values, wherein each of theN weighting elements weights each of a corresponding one of the N signalresponse values by a corresponding one of the N weighting parameters,thereby generating N weighted signal response values.
 32. The arrayprocessing module of claim 31 including: a summing portion configured toreceive the N weighted signal response values from the N weightingelements and provide a combined signal representative of the receivedsignal.
 33. The array processing module of claim 29 including: a downconversion portion coupled to each of the M signal processing chains,wherein the down conversion portion is configured to convert the Mreplicas of the received signal from radio frequency (RF) to basebandfrequency.